Page 1
AAE352 Homework Set #4 with Problem 3 updates
Due February 11, 2011
Problem #1 (Problem 41 page 74)
Problem 41Figure
a)
Develop the 4 x 4 system stiffness matrix for the three element bar shown.
b)
Use the applied loads and boundary condition to develop the 3 x 3 restrained system stiffness
matrix
c)
Find the deflections at each node due to the two applied loads
d)
Solve for the internal forces in each of the three rod elements
e)
Draw the internal forces in their correct directions for each of the three elements
f)
Compute the strain energy in the structure.
Problem #2
A configuration has four rod elements connected to three node points shown circled.
All
elements have the same Young’s modulus.
Node 1 is fixed (u
1
= 0).
The nodes move only in the
horizontal direction.
Node 2 has an applied load of 1000 lb.
Node 2 has only elements 2 and 4
attached to it.
Node 3 has three of the four elements directly attached to it.
Element 4 has one
half the crosssectional area of the other elements.
(a)
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 Fall '08
 Chen
 Chemical element, internal forces, stiffness matrix

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